Question

5. A car insurance company would like to determine the proportion of accident claims covered by the company. According to a preliminary estimate 65% of the claims are covered. How large a sample should be taken to estimate the proportion of accident claims covered by the company if we want to be 95% confident that the sample percentage is within 2% of the actual percentage of the accidents covered by the insurance company?

Answer 1

Solution :

Given that p = 0.65 , margin of error E = 0.02

=> q = 1 - p = 0.35

=> For 95% confidence interval , Z = 1.96

=> Sample size n = p*q*(Z/E)^2

= 0.65*0.35*(1.96/0.02)^2

= 2184.91

= 2185 (nearest whole number)